An Adaptative Savitzky-Golay Kernel for Laplacian Estimation in Magnetic Resonance Electrical Property Tomography

Magnetic Resonance electrical property tomography (MR-EPT) is a non-invasive imaging modality that reconstructs the living biological tissue's conductivity σ and ε_r permittivity using spatial derivatives of the measured RF field, also termed B1 data, in a magnetic resonance imaging system. The spatial derivative operator, particularly the Laplacian, amplifies the noise in the reconstructed electrical property (EP) maps, hence decreasing accuracy and increasing boundary artifacts. We propose a novel adaptative convolution kernel for generating numerical derivatives based on 3D Savitzky-Golay (SG) filters and local segmentation in a magnitude image. In comparison to typical SG kernel, the proposed kernel allows arbitrary shapes and sizes to vary with local tissue. It provides an automatic trade-off between noise and resolution, thereby significantly enhancing reconstruction accuracy and eliminating boundary artifacts.